Builders' rubble at a development in Leeds. Most of the growth in construction comes from government engineering projects, not new homes. Photograph: Christopher Thomond

Reasons to be cheerful, parts one, two and three. The economy continues to grow and one of the three main credit reference agencies has declared Britain a "stable" AAA economy.

And the third? There isn't one. And the first two are probably fake as well. That is to say, the figures showing Britain growing at a faster pace than expected and moving to a stable credit outlook hide as much as they reveal.

Underneath the GDP growth figure for the third quarter of 0.8% is a breakdown that reveals much of the boost came from construction. The sector added 4%, almost half, to the 9.5% jump in the second quarter as it recovered from the worst slump since the early 1990s. That might fuel fears that Britain is returning to the bad old days of construction-led property bubbles.

But what were the building companies doing to give such a boost to the economy? They were not building any homes; housebuilding is at record lows and residential property values are on the slide. There is a bit of commercial office construction, especially in London and the southeast, but not enough to keep the economy on track.

The busy companies, according to the most respected surveys, are working on civil engineering and infrastructure projects. A flurry of contract signings ahead of the most severe cuts in public spending appears to have played a major part in the construction figures.

Growth in construction during the second and third quarters was also boosted by the big freeze during January and February, which artificially depressed the first quarter figure.

So a property bubble is not the fear, it is the opposite. Rob Dobson of analysts Markit, said the industry has seen a significant slowdown in recent months and is unlikely to give the nation's finances a third straight quarter of growth.

"The rate of expansion is unlikely to persist, especially as public sector construction projects have driven the growth surge this year," he said. "Stripping out construction, the rate of growth of GDP is showing a sharper slowing, more in line with the surveys."

Despite the rhetoric, chancellor George Osborne kept signing cheques during the summer. It was a key reason the public finances were worse than expected last month. With cuts in public sector capital spending on the way and reforms in social housing that have left the industry unsure how to proceed, building could come to a near standstill.

Alan Clarke, UK economist at investment bank BNP Paribas, notes that industrial production could only manage 0.6% growth from the second to the third quarter, while business services were weaker than expected at 0.5%.

"The pace of industrial production has almost halved, as has business services, and the surveys point to further slowing ahead," he said. "Hold the champagne back for now – from a nation of bankers to a nation of builders? I'm not convinced."

Britain's credit rating is likely to survive any slowdown in growth, or even a double dip recession. That's because the credit ratings agencies have overcooked the problems facing Britain and its ability to repay the interest on its debts.

Arguably, the UK's credit rating was never in doubt. Panicky credit ratings agencies reacted to the Greek crisis in the spring with a scattergun, superficial assessment of the country's long-term problems. The agencies – Standard & Poor's, Moody's and Fitch – were badly hurt by the banking crisis and expect strict rules on the activities to come out of the G20 summit in a couple of weeks. With world leaders toying with restricting the activities following a few years of slapping a AAA rating on almost any financial product, it is not surprising they were more circumspect when the next crisis came along, as it did when investors asked questions about sovereign debts.

The prime minister has likened Britain to Greece on many occasions and warned of the dangers of spiralling debts. While the UK's annual debts were the highest in the G20, they fall far short of the total racked up by Germany, France and Japan.